Now, precisely how seriously are we limited by diffraction? Let us take a worst-case scenario, and assume that there is plenty of Diffraction-limited light such that the F-stop 22 is chosen. The formula for the Airy disk radius yields r = 15 µm for the middle of the visible spec trum. In other words: we get a 30 µm diameter spot on the film, photographs rather than a point. If we are using 35 mm film, we may want to enlarge the 24 by 36 mm frame by a factor of 10 in order to have L.J.F.(Jo) Hermans, Leiden University, The Netherlands a nice size picture. This means that the diffraction spots become 0,3 mm in diameter, and are no longer negligibly small. The con clusion is that, if we use high-quality optics in our camera, it may he optical performance of lenses, even in cheap cameras, is be wise to open up the lens much further and use smaller F-stop remarkably good these days. We don’t have to worry too values. Tmuch about aberrations, even if we ‘open up’ and use the full lens Now let us compare this to our digital camera: Is it the num aperture. Due to the steady progress in lens making over the years, ber of pixels that poses the limit to the resolution, or is it still our cameras - certainly the more expensive ones - are being gradu diffraction? Using the above worst-case scenario with an Airy disk ally pushed to the diffraction-limited optics situation. radius of r = 15 µm, and assuming the Rayleigh criterion for just- How does diffraction limit the resolution of our pictures? It all resolvable diffraction patterns (i.e., a spacing by r is adequate to depends, of course, on the focal length of the lens (which we usual distinguish two adjacent ones from one another), we find that, ly know) and the aperture, or effective lens diameter (which we may on a 24 by 36 mm frame, we can store be unable to determine). some 1600 x 2400 just-resolvable spots. If Fortunately, life turns out to be simple. Let us look at the we were to image that pattern on our dig- textbook formula for diffraction through a circular orifice. ital camera, and if we assume - somewhat When trying to image a point source on our film, we arbitrarily - that the pixel density must equal find that the radius of the resulting Airy disk he density of the just-resolvable spots, we need is l,22X(f/D), with A the wavelength,/the almost 4 Megapixels. This is just about the focal length and D the aperture (the performance of a modem standard digital funny numerical factor 1,22 results camera. However, if we move from the F = from integration over rectangular 22 to the other extreme of F = 2, the dif strips). fraction limited spot size shrinks by a The nice thing now is that the factor of 10. If the digital camera ratio f/D is the ‘F-stop’ value, wants to take advantage of this which we recall having used on our higher resolution, it has to increase non-automatic camera as one of its pixel number by a factor of 100. the two parameters determining So there is still room for improve the exposure. The well-known ment in the digital-camera business. series of values is 2; 2.8; 4; 5.6; 8; 11; 16; 22, spaced by V2, of course, in order to have double expo Why you shouldn't ask a sure between consecutive physicist to take your picture... values. (cartoon by W.Drenckhan)
100 europhysics news may/june 2005